Belgian authorities have released surveillance footage of Saturday's shooting at a Jewish museum in Brussels, as their hunt for the gunman who killed at least three people intensifies.

Security around all Jewish institutions in Belgium was raised to the highest level following the shooting, while French authorities also stepped up security after two Jews were attacked near a Paris synagogue.

Officials have released a 30-second video clip from the museum's security cameras showing a man wearing a dark cap and a blue jacket enter the building, take an automatic rifle out of a bag, and shoot into a room before walking out.

"From the images we have seen, we can deduce that the perpetrator probably acted alone and was well prepared," Brussels prosecutors office spokeswoman Ine Van Wymersch said.

"It's still too early to confirm whether it's a terrorist or an anti-Semitic attack, all lines of investigation are still open."

Three people - an Israeli couple and a French woman - died on the spot. AFP news agency are reporting a Belgian man, who was seriously injured in the shooting, died of his wounds on Sunday.

Officials have appealed for witnesses to the attack in the busy tourist district, which is filled with restaurants and antique shops.

The entrance to the Jewish museum was lined with flowers and candles, and will remain closed to the public on Monday.

French president Francois Hollande said the attack was without doubt motivated by anti-Semitism.